$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x - 4$ and $ JT = 9x - 12$ Find $CT$.
A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x - 4} = {9x - 12}$ Solve for $x$ $ -2x = -8$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({4}) - 4$ $ JT = 9({4}) - 12$ $ CJ = 28 - 4$ $ JT = 36 - 12$ $ CJ = 24$ $ JT = 24$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {24} + {24}$ $ CT = 48$